ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D2899
Random real number median
Formulation 0
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number.
A D993: Real number $x \in \mathbb{R}$ is a median for $X$ if and only if
(1) \begin{equation} \mathbb{P}(X \leq x) \geq \frac{1}{2} \end{equation}
(2) \begin{equation} \mathbb{P}(X \geq x) \geq \frac{1}{2} \end{equation}
Results
▶ R3738: Median need not be unique for a random real number